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arXiv · 1412.2916

Holomorphic functions unbounded on curves of finite length

Josip Globevnik
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Abstract

Given a pseudoconvex domain D in C^N, N>1, we prove that there is a holomorphic function f on D such that the lengths of paths p: [0,1]--> D along which Re f is bounded above, with p(0) fixed, grow arbitrarily fast as p(1)--> bD. A consequence is the existence of a complete closed complex hypersurface M in D such that the lengths of paths p:[0,1]--> M, with p(0) fixed, grow arbitrarily fast as p(1)-->bD.

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Josip Globevnik. 2014-12-09. Holomorphic functions unbounded on curves of finite length. https://arxiv.org/abs/1412.2916

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